In this paper the N = 4 D = 0 super Yang-Mills partition function is discussed for the case of arbitrary simple gauge group. It is explicitly evaluated in the case of orthogonal and symplectic groups with rank 4 6 N 6 11 and also for the exceptional groups F4, E6 in addition to known results. Also we suggest the answer for the case of SO(2N + 1),Sp(2N),SO(2N) groups for all N ∈ N. In addition, ...

Let (M,ω) be a connected, compact symplectic manifold equipped with a Hamiltonian SU(2) or SO(3) action. We prove that, as fundamental groups of topological spaces, π1(M) = π1(Mred), where Mred is the symplectic quotient at any value of the moment map φ.